Answer: $\dfrac{9}{5}$

Explanation:

1. Set up the elimination: The system is $5x + 14y = 45$ and $10x + 7y = 27$. Multiplying the first equation by $2$ gives $10x + 28y = 90$, so both equations now have the same $x$-coefficient.

2. Eliminate $x$: Subtracting $10x + 7y = 27$ from $10x + 28y = 90$ gives $21y = 63$, so $y = 3$.

3. Solve for $x$: Substituting $y = 3$ into $5x + 14y = 45$ gives $5x + 42 = 45$, so $5x = 3$ and $x = \dfrac{3}{5}$.

4. Find $xy$: $xy = \dfrac{3}{5} \times 3 = \dfrac{9}{5}$.

Conclusion: The value of $xy$ is $\dfrac{9}{5}$.

Note that $9/5$ and $1.8$ are examples of ways to enter a correct answer.

Common slips:

• Stopping at $y = 3$ or $x = \dfrac{3}{5}$ instead of multiplying them together.
• Multiplying the second equation by $2$ instead of the first, which does not line up the $x$-coefficients.